On the Fading Number of Multiple-Input Single-Output Fading Channels with Memory

TL;DR

This paper establishes precise bounds on the fading number of MISO channels with memory, revealing that beam-forming is asymptotically optimal at high SNR, thus advancing understanding of channel capacity limits.

Contribution

It derives new bounds for the fading number of MISO channels with memory, including a case where bounds coincide, providing exact characterization and insights into optimal beam-forming strategies.

Findings

Bounds on the fading number are tight for isotropic fading vectors.

Beam-forming is shown to be asymptotically optimal.

The fading number's precise value is obtained for certain channel distributions.

Abstract

We derive new upper and lower bounds on the fading number of multiple-input single-output (MISO) fading channels of general (not necessarily Gaussian) regular law with spatial and temporal memory. The fading number is the second term, after the double-logarithmic term, of the high signal-to-noise ratio (SNR) expansion of channel capacity. In case of an isotropically distributed fading vector it is proven that the upper and lower bound coincide, i.e., the general MISO fading number with memory is known precisely. The upper and lower bounds show that a type of beam-forming is asymptotically optimal.